How should I approach in asking my friend if she is in a relationship?

[TwiNeon]

Are you also interested in him?
Start the conversation with a "Do you remember the friend I introduced to you once?"
And depending on what she responds you continue on. If she says no, either she's not dating him, or she doesn't plan on telling you that they're going out. But if she says yes, continue on and ask " Well, I looked at his facebook the other day and now he's in a relationship. But he didn't tell me who it was." Depending on the face expression your friend does, that might hint you to the answer / Good luck and I HOPE this helps somewhat.